During the past decade, stream data mining has been attracting widespread attentions of the experts and the researchers all over the world and a large number of interesting research results have been achieved. Among them, frequent itemset mining is one of main research branches of stream data mining with a fundamental and significant position. In order to further advance and develop the research of frequent itemset mining, this paper summarizes its main challenges and corresponding algorithm features. Based on them, current related results are divided into two categories: data-based algorithms and task-based algorithms. According to its taxonomy, the related methods belonging to the different categories and sub-categories are comprehensively introduced for better understanding. Finally, a brief conclusion is given.